3D hybrid-kinetic turbulence and phase-space cascades ( in a β = 1 plasma ) Silvio Sergio Cerri Department of Astrophysical Sciences, Princeton University, USA 11th Plasma Kinetics Working Meeting WPI Vienna, 23 July - 3 August, 2018
Thanks to main collaborators M. W. Kunz (Princeton U. & PPPL) F. Califano (University of Pisa) Cerri, Kunz & Califano, Astrophys. J. Lett. 856, L13 (2018) Dual phase-space cascades in 3D hybrid-vlasov-maxwell turbulence See also: Cerri, Servidio & Califano, Astrophys. J. Lett. 846, L18 (2017) Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia
Outline 3D3V Hybrid Vlasov-Maxwell (HVM) model with electron inertia effects Evidences that kinetic turbulence is anisotropic & intermittent ok, but how much and how is it realised? Evidence that the turbulent cascade involves the entire phase space (simultaneous cascades in real and in velocity space) parallel vs/and perpendicular phase mixing Theory vs Simulations: generalised theory of ion-entropy cascade or other approaches?
3D3V HVM model + electron inertia Fully kinetic ions (Vlasov equation) Electron fluid (generalized Ohm s law w/ reduced electron inertia terms) Maxwell s equations (Faraday equation + Ampere s law w/o displacement current) Reduced mass ratio: mi / me = 100 ( de = 0.1 di ) Quasi-neutrality is assumed (ni = ne = n) An isothermal closure for electrons pressure [Cerri, Servidio & Califano, ApJL (2017)] L ~ 31 d i ; L /L = 2 ; dx = dy ~ 0.08 d i ; dz ~ d i ; dv = 0.2 v th (grid: 384 2 x 64 x 51 3 f ~ 10 TB) S. S. Cerri (Princeton U.) MPPC Workshop 25 April 2018, Princeton
Anisotropic kinetic turbulence [Cerri, Servidio & Califano, ApJL (2017)] B0 Figure: magnetic fluctuations (B0 along z)
Intermittent kinetic turbulence (i) Figure: total magnetic fluctuations δb (red), current density J (purple & surfaces), magnetic field lines (light blue)
Intermittent kinetic turbulence (ii) anisotropic and intermittent B fluctuations: [Cerri, Servidio & Califano, ApJL (2017)] anisotropic E fluctuations: kinetic-scale anisotropy: k ~ k 2/3 [ consistent with Boldyrev & Perez, ApJL (2012) ]
intermittent KAW turbulence? [Cerri, Kunz & Califano, ApJL (2018)]
intermittent KAW turbulence? [Cerri, Kunz & Califano, ApJL (2018)] ion-scale turbulence: intermittency, current sheets, spectral anisotropy & -8/3 slope critically balanced, intermittent KAW turbulence à la Boldyrev & Perez? spectral anisotropy: local vs global? ( some ongoing work with Lev and Daniel 3 persons 3 different results? )
v-space cascades of free energy LINEAR PHASE MIXING NON-LINEAR PHASE MIXING due to ballistic response of f : de-correlation of v -structures of f due to de-correlated k -fluctuations: δf ~ exp(-ik v t) slower than its nonlinear counterpart (at scales below the ion gyro-radius) mainly along B0 ( parallel ) and more important at large scales: faster than its linear counterpart, but occurring only perpendicular to B0 and only below the ion gyro-radius: [ Schekochihin et al., ApJS (2009) ] S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
v-space cascades of free energy Hermite representation of v-space cascades basis function ( Hm = Hermite polynomial of order m) 3D decomposition of the non-thermal entropy fluctuations, δf non-linear phase mixing physical argument: de-correlation of v -structures due to de-correlated k -fluctuations (does not need GK ordering) [Cerri, Kunz & Califano, ApJL (2018)]
v-space cascades of free energy Hermite representation of v-space cascades linear phase mixing ~ m -1/2 [e.g. Watanabe & Sugama, PoP (2004); Zocco & Schekochihin, PoP 2011; Kanekar et al., JPP (2015)] non-linear phase mixing ~ m -7/6 (GK theory of ion-entropy cascade in KAW turbulence) [e.g. Schekochihin et al., ApJS 2009; Cerri, Kunz & Califano, ApJ (2018)] Kolmogorov-like arguments on Vlasov eqn ~ m -3/2 or m -2 (only v-space cascades?) [Servidio et al., PRL (2017)] S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
phase-space cascades of δf [Cerri, Kunz & Califano, ApJL (2018)] Anisotropic 6D cascades! S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
phase-space cascades of δf phase-space turbulence: non-linear phase mixing argument, m ~ k 2, holds in perp phase space linear AND non-linear phase mixing are both active: parallel vs perp spectral slopes not well understood: new theory or better simulations? [Cerri, Kunz & Califano, ApJL (2018)] S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
Generalised ion-entropy cascade (i) Generalised theory of ion-entropy cascade [Cerri, Kunz & Califano, ApJL (2018)] underlying idea (Schekochihin et al., PPCF 2008): de-correlation of v -structures due to de-correlated k -fluctuations allow generalised spectral anisotropy: α = 1 standard KAW anisotropy α = 2 intermittency-corrected case α = 3 constant anisotropy assume critically balanced KAW cascade: ion-entropy non-linear timescale: weighting of the nonlinear cascade time due to ring-average in GK nonlinearity ion-entropy cascade time: small changes in the non-adiabatic GK response ( hλ ) that accumulate as a random walk to produce a change of order unity ( Δhλ / hλ ~ 1 )
Generalised ion-entropy cascade (ii) assume constant entropy flux through scales: Generalised theory of ion-entropy cascade [Cerri, Kunz & Califano, ApJL (2018)] derive scalings for non-adiabatic GK response: accounting for generalised spectral anisotropy derive phase-space spectra of ion-entropy cascade: α = 1 standard KAW anisotropy: α = 2 intermittency-corrected case: α = 3 constant anisotropy:
Generalised ion-entropy cascade (ii) ion-entropy cascade: generalisation to account for different spectral anisotropies provided NOTE: in this theory, the non-adiabatic GK response is considered to be a scalar that is passively advected by the underlying KAW fluctuations (namely, by the ExB drift due to the KAW electric-field fluctuations) able to recover a m -3/2 spectrum for kǁ ~ k, but NOT the m -2 theory of ion-entropy cascade: electrostatic vs electromagnetic? KAW-driven vs non-kaw-driven? GK vs non-gk regimes?
Summary what is the actual spectral anisotropy of kinetic turbulence? how it is realised? how do we properly measure it? how is it correctly included in the theory? how do we correctly describe kinetic plasma turbulence in phase space? electromagnetic effects needed? new theory outside GK regime? + other questions about the role of reconnection and of structures The journey just started there is some fundamental work to be done here! Thank you! S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
BACKUP SLIDES S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
Universality of kinetic-range spectrum? -1.7 Solar Wind -2.8-1.61-2.81-1.61-3.43-2.75 [ Alexandrova et al., SSR (2013) ] [ Kobayashi et al., ApJ (2017) ] [ Huang et al., ApJL (2017) ] Magnetosheath [ Chen & Boldyrev, ApJ (2017) ] -2.84-1.22-2.7-1.75-2.76
electron entropy cascade First evidence of a cascade in velocity space from in-situ data! (electron distribution function measured by MMS in the Earth s magentosheath) [ Servidio et al., PRL (2017) ]
real-space cascade of ion entropy δe effectively behaves as a passive scalar derive generalised scalings for δe spectrum: [Cerri, Kunz & Califano, ApJL (2018)] S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
2D-3V turbulence going back to 2D-3V role of reconnection B0 x y Why different large-scale properties end up in the same kinetic-range spectrum? Is this universality a signature of the same physical process that underlies the turbulent transfer at kinetic scales?
Reconnection-mediated turbulence S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
Reconnection-mediated turbulence [Cerri & Califano, NJP (2017)] Colors: J (out-of-plane current density) First suggestion that magnetic reconnection may mediates the formation of the spectral break at ion scales and the energy transfer of the turbulent cascade below the ion gyro-radius!
Reconnection-mediated turbulence [Cerri & Califano, NJP (2017)] -2.8 Colors: J (out-of-plane current density) First suggestion that magnetic reconnection may mediates the formation of the spectral break at ion scales and the energy transfer of the turbulent cascade below the ion gyro-radius!
Reconnection-mediated turbulence [Cerri & Califano, NJP (2017)] Point #1-2.8 The formation of a spectral break and of a kinetic-range spectrum is extremely fast and coincides with the time at which ion-scale current sheets undergo fast magnetic reconnection Colors: J (out-of-plane current density) see Cerri & Califano, NJP (2017)
Does this depend on large-scale details? HPIC HVM 2048 2 x 64000ppc 1024 2 x 51 3 L = 256 d i ; dx = 0.125 d i freely-decaying large-scale large-amplitude Alfvénic fluctuations (magnetic + velocity incompressible fluctuations) L ~ 63 d i ; dx ~ 0.06 d i ; dv = 0.2 v th,i continuously-driven large-scale smallamplitude partially-compressible fluctuations (only momentum fluctuations are injected) [Cerri et al., JPP (2017)] Out-of-plane ambient magnetic field B0 Comparison made for βi = 0.2, 1, and 5 Same energy-containing scales: (k di)inj 0.3 No initial density fluctuations, no initial anisotropy Isothermal electrons with Te = Ti
Does this depend on large-scale details? HPIC HVM Colors: δb (in-plane magnetic fluctuations) Very similar structures when considering the same scales Key ingredient for small-scales turbulence: reconnecting current sheets & coherent structures [Cerri et al., JPP (2017)]
Does this depend on large-scale details? Point #2 In the turbulent stage we see the same formation of coherent structures via magnetic reconnection despite completely different large-scale properties! see Cerri et al., JPP (2017) [Cerri et al., JPP (2017)]
Does this depend on large-scale details? B HPIC, B HVM B// HPIC, B// HVM β = 1 Different spectral behaviour at large scales (different setup, inizialization & forcing) Very good agreement at smaller scales (self-consisent plasma response) Numerical effects at the smallest scales (ppc-noise in HPIC, filters in HVM) [Cerri et al., JPP (2017)]
Does this depend on large-scale details? B HPIC, B HVM n HPIC, n HVM k -5/3 β = 1 k -2.9 Different spectral behaviour at large scales (different setup, inizialization & forcing) Very good agreement at smaller scales (self-consisent plasma response) Numerical effects at the smallest scales (ppc-noise in HPIC, filters in HVM) [Cerri et al., JPP (2017)]
Does this depend on large-scale details? Point #3 Self-consistent re-processing of fluctuations while they cascade perhaps same underlying process allows/mediates the kinetic cascade! [ reconnection ] see Cerri et al., JPP (2017)
Short-circuiting the cascade Tracking local current intensity increase and reconnection events [Franci, Cerri, Califano et al., ApJL (2017)] S. S. Cerri (Princeton) 11th Plasma Kinetics Workshop 23 July 2018, WPI Vienna
Short-circuiting the cascade Tracking local current intensity increase and reconnection events [Franci, Cerri, Califano et al., ApJL (2017)] The associated kinetic-range turbulent nonlinear time scale quickly adjust to the local reconnection time scale!
Short-circuiting the cascade Kinetic-scale spectrum forms before the formation of a developed MHD specturm The slopes does not change while the MHD cascade develops (amplitude just rises ) [Franci, Cerri, Califano et al., ApJL (2017)]
Short-circuiting the cascade Kinetic-scale spectrum forms before the formation of a developed MHD specturm The slopes does not change while the MHD cascade develops (amplitude just rises ) [Franci, Cerri, Califano et al., ApJL (2017)]
Connecting the dots Kinetic spectrum does not strongly depend on the large-scale properties Reconnection can allows/enhance energy transfer of turbulent fluctuations from MHD to kinetic scales (Possible non-local structure-mediated energy transfer picture? standard local nonlinear energy transfer simultaneously active? ) Enhanced total energy transfer affects spectral slopes in a way consistent with SW observations Magnetic intermittency and structures observed in the SW plasma as an intrinsic element of kinetic-scale turbulence Reconnection & turbulence as tightly entwined processes any theory of the turbulent cascade should perhaps take into account magnetic reconnection as an effective channel for energy transfer
Just 2 take-away messages Reconnection-mediated scenario for kinetic-range turbulence gets stronger (supported by an increasing number of simulations & observations) first suggestion in: Cerri & Califano, NJP (2017) + more (explicit) numerical evidences in: Franci, Cerri, Califano et al., ApJL (2017) + some theory: Loureiro & Boldyrev, ApJ (2017); Mallet, Schekochihin & Chandran, JPP (2017) Kinetic turbulence intrinsically involves the entire phase space and is anisotropic both in real- and in velocity-space! (now also supported by simulations outside GK theory & observations by MMS) first 6D anisotropic turbulent cascade in: Cerri, Kunz & Califano, ApJL (2018)